Yakk

Probably not a waterproof proof, but a good start.

The "X" character reads "contradiction" in this walkthrough.

A sees B and C, and passes.
B and C know that A would NOT pass if B=C (if B=C, then A would know A=B+C, and would know what A was)
B sees A=50 (who passed) and C, and passes
B knows B!=C because A passed
A and C know B would not pass if C=A
If (A=2C) then either (A=B+C => B=C, X) or (A+C=B) or (A+B=C). But C < A so (A+B=C) is impossible, in which case he would know (A+C=B) and have his value.
Thus, A and C know B would not pass if A=2C
C sees A=50 and B (who both passed),
C knows that he isn't A=50
C knows that he isn't A/2=25
C knows that he isn't B
C knows A!=2*C because B passed
Thus, B and A know C would not pass if B=A
If (A=2B) then either (A=B+C=>C=B X) or (A+B=C). But he passes, so X.
So, B and A know C would not pass if (A=2B)
If (A=3B) then either (A=B+C=>C=2B X) or (A+B=C) or (A+C=B). If (A+C=B) then (3B+C=B) => (C=-2B) X. So, he'd know (A+B=C) X because he didn't know the answer.
So, B and A know C would not pass if (A=3B)

A knows C!=A 2C!=A 3B!=A 2B!=A and B!=A because B and C passed
If C=4B, then either C=A+B => A=3B X or A=B+C => A=5B.

Thus, if B is 10 and C is 40, A would know he was 50 on the second round after everyone passed.

Someone want to rewrite this in a less ass-backwards manner?

__________________
Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.